Drag select with mouse
I believe that you are looking for B. B allows for exactly what you describe -- Box Select. Upon its being pressed, the cursor turns into a crosshair and awaits your  LMB dragging. Note that you can additionally use  MMB to Box Deselect.

It works as an additive or subtractitive tool, only selecting more or less, never affecting ones already selected or deselected. It works in every editor that you can select something (not just the 3D Viewport but the UV Image Editor, Graph Editor, etc.)